Addressing ambiguity in probabilistic assessments of future coastal flooding using possibility distributions
Abstract
Decisionmaking in the area of coastal adaptation is facing major challenges due to ambiguity (i.e., deep uncertainty) pertaining to the selection of a probability model for sea level rise (SLR) projections. Possibility distributions are mathematical tools that address this type of uncertainty since they bound all the plausible probability models that are consistent with the available data. In the present study, SLR uncertainties are represented by a possibility distribution constrained by likely ranges provided in the IPCC Fifth Assessment Report and by a review of highend scenarios. On this basis, we propose a framework combining probabilities and possibilities to evaluate how SLR uncertainties accumulate with other sources of uncertainties, such as future greenhouse gas emissions, upper bounds of future sea level changes, the regional variability of sea level changes, the vertical ground motion, and the contributions of extremes and wave effects. We apply the framework to evaluate the probability of coastal flooding by the year 2100 at a local, lowlying coastal French urban area on the Mediterranean coast. We show that when adaptation is limited to maintaining current defenses, the level of ambiguity is too large to precisely assign a probability model to future flooding. Raising the coastal walls by 85 cm creates a safety margin that may not be considered sufficient by local stakeholders. A sensitivity analysis highlights the key role of deep uncertainties pertaining to global SLR and of the statistical uncertainty related to extremes. The ranking of uncertainties strongly depends on the decisionmaker’s attitude to risk (e.g., neutral, averse), which highlights the need for research combining advanced mathematical theories of uncertainties with decision analytics and social science.
1 Introduction
Adaptation to future coastal flooding requires testing different adaptation pathways against different potential futures (Ranger et al. 2013; Haasnoot et al. 2013). Sea level rise (SLR) over the twentyfirst century remains uncertain (Church et al. 2013; Kopp et al. 2014, 2017). Any impact assessments should therefore include a proper uncertainty quantification.

The first facet corresponds to aleatory uncertainty. It is generally related to randomness (variability) owing either to heterogeneity or to the random character of natural processes (i.e., stochasticity) such as the occurrences of extreme storm surges. The uncertainty factor can be described in statistical terms, and the range of possible futures can be captured with probabilities using a single and unique cumulative probability distribution function (CDF);

The second facet corresponds to epistemic uncertainty. Contrary to the first type, epistemic uncertainty is not intrinsic to the system under study and stems from the incomplete/imprecise nature of the available information, i.e., the limited knowledge on the physical environment or the engineered system under study. Epistemic uncertainty encompasses a broad range of situations from the scarcity of observations to a lack of knowledge or consensus pertaining to the appropriate conceptual models or CDFs used to represent uncertainty. The latter situation corresponds to “deep uncertainty” (Lempert et al. 2003).
In the area of SLR, deep uncertainties are mostly (but not exclusively) due to a lack of knowledge regarding ice melting, particularly in Antarctica (Ritz et al. 2015; DeConto and Pollard 2016; Kopp et al. 2017), which prevents the selection of a unique CDF for future sea level rise. A proper assessment of this type of uncertainty has important implications as originally evidenced by Ellsberg (1961) since it favors situations of “ambiguity,” which most decisionmakers prefer to avoid (an effect called “ambiguity aversion”) (see also discussions by Stephens et al. (2017) and Wong and Keller (2017)).
To date, the different facets of uncertainty have mainly been addressed using the tools provided by probability theory (Hunter et al. 2013; Kopp et al. 2014, 2017; Buchanan et al. 2016; Le Cozannet et al. 2015; Horton et al. 2018) combined with expert knowledge (Church et al. 2013; Bamber and Aspinall 2013; Horton et al. 2014; Oppenheimer et al. 2016; Fuller et al. 2017). However, probabilistic approaches have limitations for properly handling deep uncertainty. Several authors (Dubois and Guyonnet 2011; Baudrit et al. 2006, 2007 and references therein, and more specifically in the climate change context in Bakker et al. 2017; Le Cozannet et al. 2017) have noted that the use of probabilities mixes the different uncertainty types into a single format, which provides information that is too precise given the available knowledge.
To overcome the shortcomings of the classic probabilistic setting, several alternative mathematical representation methods have been developed (see a comprehensive overview by Dubois and Guyonnet 2011). These methods are termed extraprobabilistic because they avoid the selection of a single CDF by bounding all the possible ones that are consistent with the available data/information. The feasibility of these approaches has been discussed for climate change impact assessments (e.g., Kriegler and Held 2005) and more recently for global SLR projections (Ben Abdallah et al. 2014; Le Cozannet et al. 2017). The latter study illustrates the concept using possibility distributions (Dubois and Prade 1988) for global projections based on the likely ranges from the IPCC Fifth Assessment Report (AR5) (Church et al. 2013) and on assumptions on highend (HE) scenarios.
On this basis, the present study goes a step further by presenting a framework for local flooding impact assessments, which combines both possibilities and probabilities to address the whole spectrum of uncertainties in addition to deep uncertainties in SLR prediction (from global to local scales). We demonstrate the applicability of these concepts to a Mediterranean coastal area in France (representative of a local lowlying urban area exposed to storm surge and waves) with a topdown approach to support decisionmaking. The proposed procedure can easily be adapted to various decision contexts and applied to other coastal areas.
We describe the case study case in Sect. 2, and we provide the principles underlying the construction of possibility distributions in Sect. 3. In Sect. 4, we jointly propagate the different sources of uncertainties, represented by probabilities or possibilities, depending on the quality and the quantity of information available. We evaluate the impact on flooding probabilities and address the following two challenges in Sect. 5: (1) the integration of the risk attitude of decisionmakers and (2) the analysis of the contribution of each source of uncertainty to the flooding probability.
2 Case study
During the twentyfirst century, h_{COAST} has been estimated following the approach of Nicholls et al. (2014), which consists of summing global SLR projections with other random variables that account for regional and local effects. This approach is justified in the Mediterranean region because (1) the complexity of processes taking place in the Mediterranean Sea prevents us from using published regional sea level projections in this area (Calafat et al. 2012; Adloff et al. 2018); (2) the published likely ranges for different regions (e.g., regional simulations of Church et al. 2013) only slightly differ (by ≈ 10 cm) from the likely ranges of global 2100 SLR projections; and (3) HE scenarios that are considered in the possibility approach (Sect. 3) rely on estimates of Antarctic melting, which remain highly imprecise today.

h_{GSLR}(RCP, HE) is the global sea level rise (GSLR). This component is affected by epistemic uncertainties, which can be categorized as deep uncertainties due to difficulties in selecting the appropriate CDF. In the following analysis, we rely on two main sources of information (see Sect. 3.2): (1) the AR5 report (Church et al. 2013) and (2) assumptions regarding highend (HE) scenarios.

h_{RSLR} is the regional deviation (RSLR) from the global mean, which partially results from the current variability in the mean sea level due to the northern Mediterranean currents and future regional variability in sea level changes (Calafat et al. 2012; Adloff et al. 2018). Apart from the central and range values of these phenomena (estimated to be 0.0 ± 0.25 m by 2070 and beyond, see Le Cozannet et al. 2015: Appendix B), the scarcity of available data prevents an unambiguous selection of a single CDF, hence introducing deep uncertainties;

h_{VGM} is the contribution of vertical ground motions, whose possible values are estimated based on an analysis of existing GNSS stations^{1} and the geology^{2}. From this analysis, only incomplete interval data can be derived. The best estimate for the range of values is evaluated, i.e., [− 2, 0 mm/year], but more extreme values ranging [− 10, + 0.4 mm/year] cannot be excluded. Given the available data, the uncertainty is categorized as epistemic;

h_{extreme} is the sum of the tidal level and the inverse barometric effect and wind setup; it is assumed to be stationary and is defined based on centennial events ranging from 1.3 to 2.0 m. The uncertainty on this component is mainly statistical in nature (aleatory) and is mathematically represented using a twoparameter Pareto distribution (Supplementary Material S5);

h_{wave} is the wave setup, which is assumed to be stationary and defined based on the combination of observations and modeling results that lead to a range of possible values: [0.4, 0.8 m] (Gervais 2012). This component is mainly of statistical nature (aleatory) and is mathematically represented using a uniform CDF (Le Cozannet et al. 2015).

Case 1 is “adaptation as usual,” where the heights of the walls are held constant (t = 2.15 m) through maintenance works whenever appropriate;

Case 2 uses a “structural adaptation” measure, for which the height of coastal defenses is assumed to have increased to t = 3.00 m by 2100, which is currently considered a maximum height to preserve the recreational value of the seafront (related to the tourism and attractiveness of the site).
3 Construction of possibility distributions
Assumptions on uncertainty representation
Uncertainty source  Type of uncertainty  Data  Representation tool  Reference 

Global SLR (GSLR)  Epistemic (deep)  Lowend, highend, likely range  Possibility distribution  Le Cozannet et al. (2017) 
RCPrelated likely range (RCP)  Epistemic (deep)  AR5 likely range conditional on the RCP scenario  Core of the GSLR possibility distribution (see Fig. 2a)  Church et al. (2013) 
Ranking of highend scenarios (HE)  Aleatory  Three scenarios (1.5, 2, and 5 m) ranked based on the representativeness of different projections available in the literature  Right tail of the GSLR possibility distribution derived from a weighed averaging scheme; the uncertainty in the weight values is represented by a Dirichlet probability distribution with shape parameters of 50, 40 and 10% (see Fig. 2c)  Le Cozannet et al. (2017): Tables 1 and 2 
Regional bias (RSLR)  Epistemic (deep)  Regional bias of ± 0.25 m  Triangular possibility distribution  Church et al. (2013); Slangen et al. (2014); Le Cozannet et al. (2015): Appendix B 
Offshore extreme water levels (Extr.)  Aleatory  Values ranging from 1.3 to 2 m for the centennial event  2parameter Pareto law  
Wave setup (wave)  Aleatory  between 0.4 and 0.8 m  Uniform distribution  Gervais (2012) 
Vertical ground motion (VGM)  Epistemic  Possible values ranging from − 2 to 0 mm/year with extreme values ranging from − 10 to + 0.4 mm/year  Trapezoidal possibility distribution with core [− 2, 0 mm/year] and support [− 10, 0.4 mm/year]. By 2100, this translates into a core [− 0.21, 0 m] and a support [− 1.05, 0.042 m] considering a reference date of 1995 (i.e., median of the reference period 1986–2005 of GSLR)  Analysis of existing GNSS stations (http://www.sonel.org/spip.php?page=gps&idStation=3193.php) and of the geology (www.infoterre.fr) 
3.1 Method
We rely on quantitative possibility theory (Dubois and Prade 1988), which is dedicated to handling incomplete information. We restrict the study to a numerical possibility distribution π : ℝ → [0, 1] to express our state of knowledge and to distinguish “what is plausible from what is less plausible” (Dubois and Prade 2016: Sect. 2.2); if π(x) = 1, then the value x is completely possible (=plausible), and if π(x) = 0, then the value x is not possible. Intervals (called αcuts) π_{α} = {e, π(e) ≥ α} contain all the values that have a degree of possibility of at least α. The intervals for α = 0 and α = 1 are called the support and the core, respectively.

the possibility of A, Π(A) = sup_{x ∈ A}π(x), measures to what extent A is logically consistent with π;

the necessity of A, N(A) = 1 − Π(A^{C}), where A^{C} is the complement of A, measures to what extent A is certainly implied by π.
Both measures link the quantitative possibilities and probabilities by expressing “what is probable should be possible and what is certainly the case should be probable as well” (Dubois and Prade 2016: Sect. 2.5), meaning that N ≤ P ≤ Π where P is the probability of the considered event. This inequality shows why this theory interestingly represents incomplete probabilistic information, either induced by statistical data or by humanoriginated estimates (see the different situations in Supplementary Materials S1).
3.2 Application
Flooding probability (probability for the coastal water level to exceed a critical threshold t) by 2100 with reference period 1986–2005, considering different procedures for uncertainty treatment
Case 1 adaptation as usual (t = 2.15 m)  Case 2 structural adaptation (t = 3.00 m)  

Joint probability and possibility propagation  [0.0–92.9%]  [0.0–27.0%] 
Postprocessing (risk neutral, w = 0.50)  13.9%  3.6% 
Postprocessing (risk averse, w = 0.75)  47.3%  6.5% 
Postprocessing (risk averse, w = 0.95)  84.3%  22.9% 
Fully probabilistic using K14*—RCP2.6  10.4%  1.4% 
Fully probabilistic using K14*—RCP4.5  13.3%  1.8% 
Fully probabilistic using K14*—RCP8.5  21.9%  3.4% 
The derived distribution (Fig. 2b) formally represents the set of CDFs (called a probability box) bounded by an upper and a lower CDF in red and black in Fig. 2b, respectively.
For the RSLR and the VGM, the available information is more limited than for the GSLR, and simpler possibility distributions are constructed (Table 1). For the RSLR, only a best estimate and the spread are known, and a triangular possibility distribution is constructed assuming a core with no deviation with respect to the global mean and a support constrained by ± 0.25 m (by 2100) in the Mediterranean Sea (Sect. 2). Similarly, only intervalvalued data are provided for the VGM, and a trapezoidal possibility distribution is defined with a core of [− 2, 0.0 mm/year] and a support of [− 10; 0.4 mm/year].
3.3 Uncertainty of the GSLR possibility distribution
The GSLR possibility distribution, though it avoids selecting a unique CDF, remains conditional on the sources of input information and is therefore itself defined by some uncertain input parameters, namely, its core and its right tail.
The first assumption is the use of the likely ranges from the AR5, which constrains the distribution core. Although the proposed framework is flexible and could include any other projection models (e.g., Kopp et al. 2014 or the recent update of 2017; Jackson and Jevrejeva 2016, among others), we chose to focus the study on the AR5 projections following the current practices of most coastal managers, who usually treat the IPCC Report as a baseline document. This choice guarantees that coastal adaptation practitioners are guided by a set of studies that have been critically assessed by the most prominent scientists in sea level science. We note, however, that a word of caution is needed with this approach, given that differences in timescales for updating sea level projections in the realms of research and operations may ultimately lead to systematic underestimations of impact and adaptation needs (Wong et al. 2017).
The likely ranges from the AR5 are conditioned on the RCP scenario. To account for the different scenarios, the core is bracketed by the minimum value of the lower bounds and by the maximum value of the upper bounds of the likely ranges from the AR5 (Supplementary Material S2). Note that from a local adaptation perspective, no preference can be given to any future climate forcing because they depend on greenhouse gas emissions that involve other levels of decisionmaking (Rockström et al. 2017).
The second assumption is related to the HE scenarios. The advantage of using a possibility distribution is to account not for specific scalar values but for intervalvalued scenarios, i.e., [0.98, 1.5 m]; [1.5, 2 m]; and [2.0, 5.0 m], hence covering a wide range of possibilities in agreement with recent studies (e.g., 99th percentile used by Kopp et al. 2017; 95th percentile used by Wong et al. 2017). The subjectivity stems, however, from the ranking values (50, 40, and 10%, as proposed by Le Cozannet et al. 2017), which constrains the distribution’s right tail. For instance, other weighting schemes may consider a stronger consensus in favor of smaller upper bounds, which can be alleviated by following the best practices in statistical studies dealing with proportion estimates (Haas and Formery 2002) through a Dirichlet probabilistic model (with shape parameters corresponding to the best estimates of 50, 40, and 10%). This procedure enables the random generation of different ranking values to reflect the uncertainty in the assumptions of Le Cozannet et al. (2017). Figure 2 (bottom) depicts some instances of the derived distributions using ranking random values. By construction, the level of this uncertainty is “statistical.”
4 Combining probability and possibility distributions
4.1 Method
We jointly propagate probability and possibility distributions using the procedure developed by Baudrit et al. (2007) (Supplementary Material S3), which combines Monte Carlo–based random sampling of inverse CDFs for random variables (h_{wave} and h_{extreme}) and of the αcuts (see Sect. 3) for the possibility distributions (h_{GSLR}, h_{RSLR}, and h_{VGM}). We slightly modify the original procedure to account for the uncertainty in the construction of the GSLR possibility distribution (Sect. 3.3) so that its right tail is newly generated at each iteration using the ranking values randomly generated from a Dirichlet distribution. At each iteration, the minimum and maximum bounds for the coastal sea level h_{COAST} are evaluated, and the result takes the form of a set of intervals (Baudrit et al. 2006), which is postprocessed in the form of a probability box.
4.2 Application
The gap between both probability bounds directly translates to “what is unknown.” This gap represents the imperfect state of knowledge in the study, which prevents the selection of a unique CDF for supporting decisionmaking regarding local flooding assessment without ambiguity. Therefore, P_{f} is not a precise and unique number but an interval; the width reflects the degree of ambiguity. For adaptation case 1, P_{f} ranges from 0.0 to 92.9%, whereas for adaptation case 2, P_{f} ranges from 0.0 to 27.0%.
For comparison purposes (Table 2), we complement the analysis with the results of a fully probabilistic analysis using the GSLR probability distribution from Kopp et al. (2014), denoted K14, conditional on RCP scenarios 2.6, 4.5, and 8.5 and assuming a triangular probability distribution for RSLR and VGM. In case 1, the K14 probabilistic approach shows that P_{f} ranges from ≈ 10 to 22% depending on the RCP scenario choice. Though this range is relatively wide, it still underestimates the gap of imperfect knowledge as highlighted by the proposed approach (i.e., with a wider range of > 90%). Clearly, the lack of knowledge related to all uncertain factors results in a situation with a very high degree of uncertainty, which makes the selection of a unique CDF barely achievable. Had the overall uncertainty been summarized using a single probability value, this problem would have been masked.
With structural adaptation (case 2), the range considering the three distributions of K14 is lowtomoderate ([≈ 1.4, 3.4%]), which suggests limited ambiguity in the quantified flooding hazard estimates. However, this result may give a greater degree of certainty than warranted. The nonnegligible range of 27% provided by the proposed approach nuances this result and suggests that ambiguity resulting from uncertain factors should be incorporated into the decisionmaking process (see Sect. 5.1).
5 Impact on the flooding probability
5.1 Integrating risk aversion
The advantage of the proposed approach is to measure the degree of ambiguity in P_{f} (i.e., the width of the probability interval). The degree of ambiguity turns out to be so large in our case (Sect. 4.2) that it can hinder the decisionmaking process. In this situation, the decisionmaker may adopt different attitudes. Highly risk averse decisionmakers may prefer to rely on the pessimistic bounds. However, this criterion may be too conservative because it neglects the information that leads to less pessimistic outcomes. This limitation justifies using decisionmaking criteria, which balance plausible and worstcase scenarios to derive an “effective” probability, similar to the limited degree of confidence criterion adapted for allowance estimates by Buchanan et al. (2016).
Following a similar idea, we rely on the criterion proposed by Dubois and Guyonnet (2011) to provide a single “effective” CDF. This CDF is derived by calculating the weighted average of the upper and lower bounds of the probability box considering different quantile levels from 0 to 100% (i.e., “horizontal” cuts). The weight w reflects the risk attitude of the decisionmaker (i.e., the degree of risk aversion). If w = 1.0, more weight is given to the pessimistic bound (the black CDF in Fig. 3b), and the level of risk aversion of the decisionmaker is the highest. If w = 0.0, the decisionmaker is riskprone and uses the optimistic bound. A w = 0.5 corresponds to a neutral attitude; i.e., the decision is based on both optimistic and pessimistic bounds without a preference between them (the green CDF in Fig. 3b). The postprocessing phase results in a single probability value P_{w}, which reflects both the imprecise nature of P_{f} and the risk attitude (aversion) of the decisionmaker.
The benefit of our approach is to introduce “subjectivity” into the CDF selection only at the end of the uncertainty treatment, i.e., once the whole spectrum of uncertainty has been propagated and summarized in the form of a probability box. If the selection had been performed at the beginning of the uncertainty analysis, this initial assumption would have ultimately been lost in the propagation process, and the final result would not have been able to keep track of it (Dubois and Guyonnet 2011). For case 2, P_{w} reaches 3.6% (risk neutral, w = 0.50), which is the same order of magnitude as the K14 probabilistic results, hence suggesting a low flooding hazard zone. However, an increase in the risk aversion (P_{w} = 6.5% and P_{w} = 22.3% for w = 0.75 and 0.95, respectively) further suggests a nonnegligible impact of ambiguity and a need for a critical reflection on the input information (following the recommendation by Dessai and Hulme 2004).
5.2 Influence of the different uncertainty sources
A broad width of the P_{f} interval requires an exploration of the role of each uncertainty source in the decisionmaking process to assess to what extent future research may reduce these uncertainties. We aim to identify which uncertain factors affect P_{w} the most and while considering different risk attitudes. We conduct a sensitivity analysis based on the pinching approach of Ferson and Tucker (2006), which consists of evaluating how P_{w} evolves when each factor’s distribution is perturbed in turn (by fixing the considered CDF to a given quantile value or by fixing the considered possibility distribution to a given αcut) (see the details in Supplementary Material S4).
Figure 4 also highlights the key role of the decisionmaker’s risk attitude (i.e., the weight w). In case 1, Fig. 4 (top) shows that P_{w} is more impacted by a change in w than by any perturbation of the input factors. Changes in the GSLR uncertainty representation would lead to only a ≈ 30% decrease in P_{w} (Fig. 4b, c), whereas an increase in w from 0.75 to 0.95 results in a large increase (of ≈ 50%) in P_{w}. This result means that, regardless of the decrease in the input uncertainty, an expected improvement of scientific knowledge would not help the decisionmaking process that much, which more strongly depends on the decisionmaker’s attitude toward risk. However, in case 2, the impact of w is less pronounced, and P_{w} is driven by the scientific information received by the decisionmaker. A better knowledge of key factors (in particular, GSLR) would, in that case, reduce the influence of risk aversion and therefore ease the decisionmaking process.
6 Discussion, concluding remarks, and ways forward
The current case study discusses the benefits of using distinct tools for uncertainty representation depending on the available data. A handful of methods exist to address this problem, but many lack practical recommendations to bring them to an operative state (as outlined by Flage et al. (2014) in their concluding remarks). Our work aims to fulfill this requirement by providing practical recommendations on how to (1) use the possibility distribution derived from the IPCC information to avoid making prior assumptions regarding the nature of the CDF; (2) implement uncertainty propagation from sea level rise to the coastal impact; and (3) provide users different and complementary information from the probabilistic and possibilistic viewpoints.
Specifically, our results highlight where the current knowledge prevents the assignment of a unique CDF to future flooding risks (Fig. 3). Within a topdown approach, we propose to inform the decisionmaker with a single “effective” CDF, which reflects not only the impact of ambiguity but also his/her attitudes toward risk. If a large ambiguity exists, the procedure can ultimately rely on a sensitivity analysis to identify research areas where reducible uncertainty remains. The proposed approach constitutes the basis to extend the applicability of the proposed framework to decision contexts starting from the impact (e.g., flood damages) within a bottomup approach, but without necessarily relying on probabilities (see the discussion by Dessai and Hulme 2004).
Our application shows that the benefit of the scientific information provided to decisionmakers differs depending on the adaptation case. In the “adaptation as usual” case, the decision regarding coastal flooding management mostly depends on the attitude to risk; in the “structural adaptation” case, the flooding probability is more impacted by variations in the uncertain factors than in the “adaptation as usual” case and, more specifically, the amount of knowledge on the GSLR. These results call for strong interactions among the different actors, as underlined by other studies (e.g., Buchanan et al. 2016). Today, such interactions between scientific information, decisionmakers, and users are recognized as essential in order to support adaptation (Monfray and Bley 2016). However, in the area of coastal adaptation, further research involving climate, coastal, and social science, as well as behavioral and decision analytics, is needed to evaluate to what extent the proposed uncertainty treatment framework can support the resolution of the problem of coastal adaptation (Bisaro and Hinkel 2016). With this view, the proposed possibilitybased approach could provide a good basis to trigger and structure discussions on sea level rise uncertainties among experts of different horizons by providing viewpoints that supplement or complement those of probabilities. The proposed approach could constitute a key ingredient of future expert elicitation exercises, as done, for instance, by Bamber and Aspinall (2013) using probabilities. As discussed by Cooke (2004), this direction will require further research to strengthen the links between the possibility and decision theories. We argue that using the rigorous setting proposed by Dubois et al. (2001), for instance, can be a way forward to reach an operative state in this area.
Footnotes
Notes
Acknowledgments
We thank Alexander Bisaro, Patrick Bazin, Dominique Guyonnet, Jochen Hinkel, Déborah Idier, Carlos Oliveros, Rodrigo Pedreros, Robert Nicholls, and the WCRP Grand Challenge “SeaLevel Rise and Coastal Impacts” for useful discussions on coastal risks, decisionmaking, and uncertainties. Implementation of the methods was performed using the R package HYRISK^{3}.
Funding information
This study received financial support from BRGMfunded project DEVEXTRAPOLATE (inkind contribution to the Convention Services Climatiques of the MTES) and ERA4CS/ECLISEA (Grant 690462).
Supplementary material
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